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Home » Out of 6 teachers and 8 students, a committee of 11 is being formed. In how many ways can this be done, if the committee contains (i)exactly 4 teachers? (ii)at least 4 teachers?
Out of 6 teachers and 8 students, a committee of 11 is being formed. In how many ways can this be done, if the committee contains
(i)exactly 4 teachers?
(ii)at least 4 teachers?
Rs aggarwal Maths CBSE Class 11 Chapter 9 Exercise 9B
Out of 6 teachers and 8 students, a committee of 11 is being formed. In how many ways can this be done, if the committee contains
(i)exactly 4 teachers?
(ii)at least 4 teachers?

Answer : Since the committee of 11 is to be formed from 6 teachers and 8 students.

  • Forming a committee with exactly 4 teachers Choosing 4 teachers out of 6 in 6C4 Remaining 7 from 8 students in 8C7 ways.

Thus, total ways in (i) are 6C4      8C7 ways.

  • The number of ways in this case is
  1. 4 teachers and 7 students
  2. 5 teachers and 6 students
  3. 6 teachers and 5 students

= 6C4 X8C7+ 6C5 X8C6 X6C6 X8C5

= 344 ways

 

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